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\title{Daily progress report 4}
\author{Hylke Buisman}

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\section{Introduction}
This document serves to report the progress that was made in the remainder of the second week.
This will mainly consist of a small abstract from my Wiki\footnote{http://hbuisman.wetpaint.com/}, 
which contains more detailed and up to date info on my progress. 
The next sections present a small logbook and a short summary of my activities.

\section{Logbook}

\begin{table*}[h]
	\centering
		\begin{tabular}{ccp{3.5in}}
		\textbf{Day} & \textbf{Hours} & \textbf{Activities}\\
		\hline \\
		June 14 & 8 & Redid clusters + causal paths + layout report\\
		June 15 & 8 & Meeting Bert + rest naive U-tube solution excl. ternary relations\\
		June 16 & 2 & Cleaned up documentation + start report\\
		June 17 & 2 & Worked on progress reports + midterm progress report\\
		\end{tabular}
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\section{Summary}
First of all I mainly spent my time on optimizing the causal path finding.
In order to do this we decided that clusters formed the basis for finding causal paths.
In addition I explored ways of combining causal paths within clusters. Restrictions
had to be applied to prune the possible models. Clusters are now found differently than before.
Q-correspondences and proportionalities are the basis for a cluster. Besides that, clusters
can not consist of quantities from different entities. This approach is more
efficient than before. We decided that clusters would be linked together first from within the entity it belongs to,
and then from other entities.

On Friday the implementation returned 9 possible models for the U-Tube model.
The result is quite satisfying, since all returned models comply with the data, and
a subset could not be returned without further knowledge. However, the subtraction
was not included yet.

In the weekend I worked on administrative tasks like completing my progress reports,
and working on the project report.

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